It was shown decades ago that a radical pair reaction with anisotropic hyperfine interactions would exhibit sensitivity to external magnetic fields - even fields as weak as the geomagnetic field - see [T. Ritz, S. Adem & K. Schulten; Biophys. J., 78, 707-718 (2000)] or [K. Schulten, C. E. Swenberg & A. Weller; Zeitschrift für Physikalische Chemie, 111, 1-5 (1978)]. So far only model systems has been studied, but we want to investigate whether such a chemical compass mechanism can be realized in a real molecular system, in particular the photoreceptor proteins cryptochromes.
A radical pair can be generated by photoexcitation and a subsequent electron transfer - this is the case in cryptochrome - and such a radical pair will be generated in a coherent spin state, i.e. singlet or triplet. The initial state of the radical pair will depend on the spin state before photoexcitation; a system in the singlet state will lead to a radical pair in the singlet state.
Once the radical pair is created it is subjected to various interactions, and the spin state of the radical pair may therefore change over time. In addition to these interactions, it may react chemically, possibly eliminating the radical pair by recombination. These reactions may be spin dependent, i.e. some reactions may be forbidden in the singlet state but allowed from a triplet state, and vice versa, and we may therefore construct a simple reaction scheme as in Figure 1 below.
Figure 1. A simple radical pair reaction scheme. Singlet states are red, triplet blue.
As is seen in the figure above, the interactions in the system leads to interconversion between singlet and triplet spin states of the radical pair. These interactions are mainly magnetic: external magnetic fields may interact with the radicals through the Zeeman interaction, the radicals may interact with the magnetic fields produced by the spins of nearby nuclei through the hyperfine interaction, the two radicals may interact with each other through the magnetic dipole-dipole interaction and the exchange interaction, etc.
One of the most important interactions for the chemical compass is the hyperfine interaction: due to the conservation law of angular momentum (spin is an intrisic angular momentum - a quantum mechanical property of elementary particles), interconversion between singlet and triplet states cannot happen unless it is accompanied by an "opposite change" in the environment; e.g. a nuclear spin may change its spin state at the same time. Thus without hyperfine interactions with nearby nuclei, the radical pair would be stuck in the initial state.
Once we have hyperfine interactions, other interactions such as with an external magnetic field may affect the singlet-to-triplet conversion rate, and thereby shift the distribution of singlet and triplet states. Thus for a model such as Figure 1 above, an external magnetic field would influence the ratio of singlet and triplet products generated by the radical pair. But what if we now rotate our system? That would change the external magnetic field without changing the internal magnetic fields generated by the nuclear spins (from the point of view of the molecular system), and therefore the modulation of the singlet-to-triplet conversion rate caused by the external magnetic field would change - and as a result, the ratio between singlet and triplet products would change.
The change in the ratio of singlet and triplet products obtained by rotating the molecular system provides our compass: if we measure this ratio of the products for different orientations of the molecular system, we could infer the direction of the external magnetic field from these data.
Figure 1 shows just one possible model for the radical pair mechanism; there are many possible models, and it remains to be shown which model is actually used for magnetoreception.